Rational approximation of pi

Question

I found this problem intriguing: $355 / 113 = 3.14159292035398\ldots$ gives the approximation of $\pi$ in $7$ correct numbers, say $C(355/113)=7$, but it number of digits in numerator + number of digits in denominator is six, say $L(355/113)=6$. How many rationals $a/b$ there are such that $L(a/b)<C(a/b)$?

The best rational approximations for a number are drawn from its continued fraction expression. — Lucian, Jan 09 '15 at 13:59
http://math.stackexchange.com/questions/180073/approximating-pi-with-least-digits?rq=1 — draks ..., Jan 09 '15 at 14:06

score 2 · Answer 1 · answered Mar 25 '15 at 05:54

2

Here is a few OEIS sequences which may help answer this question:

A002485 https://oeis.org/A002485 A002486 https://oeis.org/A002486

I hope this helps.

answered Mar 25 '15 at 05:54

John Nicholson

518

Rational approximation of pi

1 Answers1